The present paper examines the role of exact results in the theory of many-body physics, and specifically the example of the Mermin-Wagner theorem, a rigorous result concerning the absence of phase transitions in low-dimensional systems. While the theorem has been shown to hold for a wide range of many-body models, it is frequently ‘violated’ by results derived from the same models using numeri...

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...

For a connected graph G = (V (G), E(G)) and two disjoint subsets of V (G) A = {α1, . . . , αk} and B = {β1, . . . , βk}, a paired (many-to-many) k-disjoint path cover of G joining A and B is a vertex-disjoint path cover {P1, . . . , Pk} such that Pi is a path from αi to βi for 1 ≤ i ≤ k. In the recent paper [Disjoint Path Covers in Cubes of Connected Graphs, Discrete Mathematics 325 (2014) 65–7...

In this paper, an interesting and easy method to solve the multi-dimensional  knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA).  Finally, ite...

Although mathematical literacy self-efficacy (belief that one can do mathematics) is essential to success in learning mathematics, it not explicitly addressed many educational institutions. The current paper used Reigeluth’s Model of increasing achievement and for literacy. It the models depend on constructivist theory contributes helping student link his or her previous information with new ex...

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

We introduce the notion of a Bishop topological group i.e., X equipped with topology functions F such that operations are morphisms respect to F. A closed subset in neighborhood structure induced by its is defined positive way not as complement an open X. The corresponding closure operator, although it topological, classical sense, does involve sequences. As countable choice (CC) avoided, and a...